Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Free Probability and Random Matrices Seminar

Probability Seminar - Jamie Mingo (Queen's University)

Tuesday, February 11th, 2020

Time: 1:00-2:00 p.m.  Place: Jeffery Hall 202

Speaker: Jamie Mingo (Queen's University)

Title: A Survey of the Weingarten Calculus.

Abstract:  The Weingarten calculus is a method for calculating the expectation of products of entries of Haar distributed unitary (or orthogonal) matrices. The basic tool is Schur-Weyl duality, however I will present an approach based on Jucys-Murphy operators. The Weingarten calculus started with Don Weingarten in 1978. Many authors have contributed since then. This talk will be based on papers of Collins, Sniady, and Zinn-Justin.

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Probability Seminar - Sang-Gyun Youn (Queen's University)

Wednesday, May 1st, 2019

Time: 3:30-5:00 p.m.  Place: Jeffery Hall 319

Speaker: Sang-Gyun Youn (Queen's University)

Title: Minimum output entropy and capacities of quantum channels.

Abstract:  In this talk, minimum output entropy (MOE) and Holevo/quantum capacity of quantum channels will be discussed. And I will sketch how the additivity conjecture of MOE was disproved by random unitary channels.

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Probability Seminar - Jamie Mingo (Queen's University)

Monday, January 21st, 2019

Time: 10:00-11:30 a.m.  Place: Jeffery Hall 319

Speaker: Jamie Mingo (Queen's University)

Title: Tensor Products of Modules and Vector Spaces.

Abstract:  This talk will review the construction of the tensor product of modules and its universal property. This property can be used to establish associativity, commutativity over direct sums, and a check for linear independence when our modules are vector spaces. I also hope to give a brief introduction to tensor norms.

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Probability Seminar - Sang-Gyun Youn (Queen's University)

Thursday, November 29th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

Speaker: Sang-Gyun Youn (Queen's University)

Title: Some questions on Jones-Wenzl projections in view of quantum information theory.

Abstract:  It is very natural to study separability or PPT property of quantum states in view of quantum information theory and the need to study those properties for so-called Jones-Wenzl projections has emerged in recent years. In this talk, I am going to introduce the notions of separability, PPT property and Jones-Wenzl projections.

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Probability Seminar - Pei-Lun Tseng (Queen's University)

Thursday, October 18th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

Speaker: Pei-Lun Tseng (Queen's University)

Title: Right Hilbert A-modules, Part II

Abstract:  For the last talk, we gave some motivating examples and the definition of right A-module. We will begin this talk by showing some properties of A-valued pre inner product, and then we will deduce the process to construct a right Hilbert A-module. Next, we will introduce the operators on right Hilbert A-modules, and proving some properties of the corresponding adjoint operators.

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Probability Seminar - Pei-Lun Tseng (Queen's University)

Thursday, October 11th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

Speaker: Pei-Lun Tseng (Queen's University)

Title: Right Hilbert A-modules

Abstract:  Last week, we gave a sketch of proving the GNS construction. We will start to introduce the matrices over a C*-algebra this week, which is an application of the GNS construction. Then, we will begin the new topic: Right Hilbert A-modules. We will deduce the process to construct the inner product on a right Hilbert A-module H. As long as we have the inner product, we can consider the orthogonality on H and compare the different between the scalar case and $A$-valued case.

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Probability Seminar - Pei-Lun Tseng (Queen's University)

Thursday, October 4th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

Speaker: Pei-Lun Tseng (Queen's University)

Title: A-Valued Theory

Abstract:  In order to study operator-valued probability, we need some basic knowledge of C*-algebras. In this talk, I am trying to review what is a C*-algebra. and some properties of C*-algebras. The GNS construction will be covered, which is known as the follows: every C*-algebras can be represented as a algebra of bounded linear operators on a Hilbert space. This construction gives us good starting point to study matrices over a C*-algebra. If time permits, I will introduce right Hilbert A-modules.

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